In ecclesiastical language, the state or the abode of temporary punishment for those souls, who having died in the state of grace, are not entirely free from venial sins or have not yet fully paid the satisfaction due to their transgressions. It is not a state of positive growth in goodness and in merit, but of purification effected by suffering. The Catholic doctrine, defined at the Council of Florence and repeated at the Council of Trent, is

there is a Purgatory

the souls suffering there can be helped by the prayers of the faithful, especially by the Sacrifice of the Altar

Although Holy Scripture does not expressly mention Purgatory, it presupposes it, and refers to it clearly enough, e.g., 2 Machabees 12; Matthew 5 and 12; 1 Corinthians 3; Philemon 2; 1 Peter 3. Purgatory is firmly established by tradition and confirmed by the constant belief of the Church in suffrages for the dead. The chief punishment consists in being deprived of the beatific vision (pæna damni). Besides this there is the additional punishment (pæna sensus), which, according to the common belief of the Western Church, consists in real fire. They are certain of their salvation, and are confirmed in good, hence can no longer sin. Since they love God perfectly, they bear their sufferings with resignation. This love of God and resignation to His holy Will, according to many theologians, considerably lessens and mitigates the severest sufferings of Purgatory. In the early Church some heretics denied the existence of Purgatory. In the Middle Ages the Cathari, Waldenses, and Hussites rejected it, and in the 16th century Luther and Calvin and their followers did the same. Protestants, therefore, generally reject it. The Greeks have a vague and indefinite notion of it. Belief in Purgatory fosters piety. It deters man from venial sin, begets a spirit of penance, gives him occasion to practice charity to the dead, and awakens salutary thoughts of the life to come.

All who die in God’s grace and friendship, but still imperfectly purified, are indeed assured of their eternal salvation; but after death they undergo purification, so as to achieve the holiness necessary to enter the joy of Heaven. — Catechism of the Catholic Church, par. 1030

It cannot be doubted that the prayers of the Church, the Holy Sacrifice, and alms distributed for the departed relieve those holy souls and move God to treat them with more clemency than their sins deserve. It is the universal practice of the Church, a practice that she observes as having received it from her forefathers — that is to say, the holy Apostles. — Saint Augustine of Hippo